Either steam broccoli or place the broccoli in a microwave safe glass dish covered with a damp paper towel and cook on high for 3 minutes. Optional: immediately chill under cold water to keep color and stop the cooking process. Separate into 2 batches, reserving 1/2 cup for garnishing. Set aside.
To make the roux, melt the butter in a large stock pot. Add the flour and whisk to allow flour to absorb the butter and turn a light golden color, cooking and bubbling for several minutes on medium-low heat.
Add white pepper and chicken stock, and whisk constantly to ensure thorough incorporation and no lumps. Season with kosher salt.
Bring the thickened chicken stock to a boil and add the onion and cook for 3 minutes, then add the nutmeg and steamed broccoli.
Using a soup ladle, add soup to a blender along with the half and half cream and puree. Purée with lid slightly ajar to allow steam to escape. Pour this mixture back into the stock pot to simmer and keep warm until serving.
Serve with remaining steamed broccoli on top, a drizzle of good olive oil and crusty French bread.